Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer:
`y=-x-6`

Explanation:

The formula for slope-intercept is
`y=mx+b`, with
`m` representing the slope,
`b` being the y-intercept, and
`x` and
`y` representing inputs and outputs of the line.

To write the equation of a line in slope-intercept form, you need two components:

1. The slope (
`m`), which describes the steepness and direction of the line.
2. The y-intercept (
`b`), or the point at which the line intersects the y-axis.

There are two methods to find slope. The first is by using the equation
`m = (x_(2)-x_(1))/(y_(2) -y_(1))`, with
`(x_(1), y_(1) )` and
`(x_(2), y_(2))` being two points on the line. In the second method, you look at the graph and find the rise over run (
`(rise)/(run)` ) for two points on the line.

In this instance, let’s use the formula. The two points on the line I’ll use (you can choose any two points) are
`(0,-6)` and
`(-6,0)`. Input them into the equation and you get the following:

`m=(-6-0)/(0- (-6))`

`m = (-6)/(6)`

`m=-1`

To find the y-intercept, look on the graph and find where the line intersects the y-axis, or the vertical axis. The point at which the line intersects the y-axis is
`(0,-6)`; therefore, the y-intercept is -6.

Input the slope and y-intercept into the equation and you get the following:
`y=-x-6`. This is our finial answer.